Quantum cosmological perfect fluid model and its classical analogue

The quantization of gravity coupled to a perfect fluid model leads to a Schr\"odinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state $p = \alpha\rho$; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid. The meaning of the existence of this universal classical analogue is discussed. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of $\alpha$, while the radiative non-flat case is equivalent to the harmonic oscillator. The repulsive fluid needed to reproduce the quantum results is the same in both cases.Comment: Latex file, 13 page

Ácido giberélico no raleio de cachos de uva da cv. superior seedless, enxertada sobre o porta-enxerto 'SO4', cultivada na região do Vale do Submédio São Francisco Giberelic acid in grape cluster thinning, cv. superior seedless, grafted on the rootstock "SO4", cultivated at São Francisco Valley

Com o objetivo de avaliar o efeito de concentrações de ácido giberélico no raleio e melhoria da qualidade de cachos de uva da cv. Superior Seedless, foi realizado este experimento em pomar comercial na Fazenda Copa Fruit S.A., município de Petrolina-PE. o delineamento experimental foi em blocos ao acaso, com sete tratamentos (GA3: 0,0; 0,5; 1,0; 2,0; 4,0; 6,0 e 8,0 mg.L-1), quatro repetições e duas plantas por parcela, e os dados foram interpretados por meio de análise de variância e regressão. As aplicações dos tratamentos foram realizadas em três fases, a primeira antes da antese e a segunda e terceira com aproximadamente25% e 80% de flores abertas, respectivamente, utilizando-se de um volume de calda de 2.000 litros/ha. Os cachos foram colhidos com 60 dias após a poda, e as características avaliadas foram: comprimento médio de cacho, engaço e "ombros"; densidade de bagas; massa da matéria fresca do cacho e bagas; e diâmetro e comprimento de bagas. os melhores resultados para o raleio foram obtidos com a concentração de 0,5 mg.L-1, que proporcionou uma densidade de 5,39 bagas/cm de cacho, contra 8,24 bagas/cm de cacho obtido pela testemunha. Em relação à melhoria da qualidade de cachos e bagas, aplicações de GA3 acima de 2,0 mg.L-1, apesar de mostrarem eficiência no aumento do comprimento de cachos, tiveram efeitos negativos na massa da matéria fresca de cachos e bagas, inviabilizando os cachos comercialmente.<br>With the objective to evaluate the effect of concentrations of gibberellic acid in thinning and in the quality improvement in grape clusters cv. Superior Seedless it was carried out an experiment in a commercial orchard in Copa Fruit S.A. farm, in Petrolina-PE. The experiment was arranged in a completely randomized design, with seven treatments (GA3: 0.0, 0.5, 1.0, 2.0, 4.0, 6.0 and 8.0 mg.L-1), four replications and two plants/plot, and the data were interpreted by analysis of variance and regression. The applications of the treatments had been carried out in three phases, the first one before the flower opening and the second and the third with approximately 25% and 80% of flowers opened, respectively, using a volume of 2.000 liters per hectare. The clusters had been harvested with 60 days after pruning and the evaluated characteristics had been: average length of cluster, stem and "shoulders"; density of berries/cm of cluster; mass of fresh matter of the cluster and berries; e diameter and length of berries. The best results for thinning had been gotten with the concentration of 0.5 mg.L-1, which provided a density of 5.39 berries/cm of cluster, from 8.24 berries/cm of cluster gotten from the witness. In relation to the improvement of the quality of clusters and berries, applications of GA3 above of 2.0 mg.L-1, although will show efficiency in the increase of the length of the cluster, had negative effect in the mass of fresh matter of clusters and berries, making the clusters commercially impracticable

Consumo, digestibilidade de nutrientes e balanço de nitrogênio da silagem de capim-elefante com adição de pedúnculo de caju desidratado Intake, nutrients digestibility and nitrogen balance of elephant grass silages added different levels of dehydrated cashew stalk

A presente pesquisa foi realizada com o objetivo de avaliar o valor nutritivo de silagens de capim-elefante contendo níveis crescentes de pedúnculo de caju desidratado (PCD). Foram utilizados 20 ovinos machos e não castrados, seguindo o delineamento experimental inteiramente casualizado, com cinco tratamentos (níveis de adição de 0; 4; 8; 12 e 16%) e quatro repetições. Foram avaliados os consumos e a digestibilidades da matéria seca (MS), da matéria orgânica (MO), da proteína bruta (PB), da fibra em detergente neutro (FDN), da fibra em detergente ácido (FDA), do extrato etéreo (EE), dos carboidratos totais (CHT), dos carboidratos não fibrosos (CNF), além do valor de nutrientes digestíveis totais (NDT) e do balanço de nitrogênio (BN) das silagens. A adição de PCD não influenciou os consumos de MS, MO, FDN, FDA, CHT e NDT expresso em % PV e g kg-1 PV0,75 e as digestibilidades da MO, PB, FDN, FDA e CHT das silagens. No entanto, a adição do PCD promoveu aumento nos consumos de PB, EE e CNF (% PV e g kg-1 PV0,75), nas digestibilidades do EE e dos CNF e no valor de NDT e balanço de nitrogênio. Por outro lado, a inclusão de PCD na ensilagem do capim-elefante promoveu efeito linear decrescente na digestibilidade da FDA das silagens. Conclui-se que as silagens com adição de PCD podem ser utilizadas como volumoso para ruminantes em razão das melhorias nos consumos de PB, EE e CNF e nas digestibilidades do EE e dos CNF, além do valor de NDT e BN das silagens, recomendando-se a adição de até 16% na matéria natural.<br>The nutritive value of elephant grass silages, with increasing levels of dehydrated cashew stalk (DCS) was evaluated. Five addition levels were studied (0; 4; 8; 12 and 16%), using 20 rams in a completely randomized design with five treatments (addition levels) and four replicates (animals). Intake and digestibility of dry matter (DM), organic matter (OM), crude protein (CP), neutral detergent fiber (NDF), acid detergent fiber (ADF), ether extract (EE), total carbohydrates (TC) and non-fibrous carbohydrates (NFC) were determined, as well as total digestible nutrients (TDN) and silages nitrogen balance (NB). DCS did not affect intakes of DM, OM, NDF, ADF, TC and TDN, neither digestibility of OM, CB, NDF, ADF and TC silages. Otherwise, the addition of DCS increased intakes of CP, EE and NFC and digestibility of EE, NFC, as well as TDN values and nitrogen balance. Inclusion of DCS showed linear decreasing digestibility of ADF. It is concluded that addition of DCS to silages of elephant grass up to 16% on a natural basis can be used as a forage source for ruminants